Related papers: Balancing adaptability and predictability: K-revis…
This paper presents an adaptive horizon multi-stage model-predictive control (MPC) algorithm. It establishes appropriate criteria for recursive feasibility and robust stability using the theory of input-to-state practical stability (ISpS).…
We study two-stage adjustable robust linear programming in which the right-hand sides are uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the affine policy is a popular, tractable approximation. We…
Decision rules offer a rich and tractable framework for solving certain classes of multistage adaptive optimization problems. Recent literature has shown the promise of using linear and nonlinear decision rules in which wait-and-see…
Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to realizations that are uncertain. Algorithms designed to address multistage stochastic linear…
We study piecewise affine policies for multi-stage adjustable robust optimization (ARO) problems with non-negative right-hand side uncertainty. First, we construct new dominating uncertainty sets and show how a multi-stage ARO problem can…
We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…
Two-stage robust optimization is a fundamental paradigm for modeling and solving optimization problems with uncertain parameters. A now classical method within this paradigm is finite adaptability, introduced by Bertsimas and Caramanis…
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…
Choosing control inputs randomly can result in a reduced expected cost in optimal control problems with stochastic constraints, such as stochastic model predictive control (SMPC). We consider a controller with initial randomization, meaning…
In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with non-Lipschitzian value…
In this paper, we propose novel mixed-integer linear programming (MIP) formulations to model decision problems posed as influence diagrams. We also present a novel heuristic that can be employed to warm start the MIP solver, as well as…
This paper introduces a multi-timescale stochastic programming framework designed to address decision-making challenges in power systems, particularly those with high renewable energy penetration. The framework models interactions across…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
We introduce a dynamic approach to probabilistic forecast reconciliation at scale. Our model differs from the existing literature in this area in several important ways. Firstly we explicitly allow the weights allocated to the base…
We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this,…
We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive…
Uncertain optimization problems with decision dependent information discovery allow the decision maker to control the timing of information discovery, in contrast to the classic multistage setting where uncertain parameters are revealed…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions…